Theory of the NS-$\overline{\omega}$ model: A complement to the NS-$\alpha$ model

W. Layton; Iuliana Stanculescu; Catalin Trenchea

doi:10.3934/cpaa.2011.10.1763

Article Contents

2011, Volume 10, Issue 6: 1763-1777. Doi: 10.3934/cpaa.2011.10.1763

This issue Previous Article A Liouville comparison principle for solutions of singular quasilinear elliptic second-order partial differential inequalities Next Article Even solutions of the Toda system with prescribed asymptotic behavior

Theory of the NS-$\overline{\omega}$ model: A complement to the NS-$\alpha$ model

1.
University of Pittsburgh, Department of Mathematics, Pittsburgh, PA 15260
2.
Farquhar College of Arts and Sciences, Nova Southeastern University, Ft. Lauderdale, FL 33314
3.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260

Received: June 2010

Revised: March 2011

Published: November 2011

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Abstract

We study a recent regularization of the Navier-Stokes equations, the NS-$\overline{\omega}$ model. This model has similarities to the NS-$\alpha$ model, but its structure is more amenable to be used as a basis for numerical simulations of turbulent flows. In this report we present the model and prove existence and uniqueness of strong solutions as well as convergence (modulo a subsequence) to a weak solution of the Navier-Stokes equations as the averaging radius decreases to zero. We then apply turbulence phenomenology to the model to obtain insight into its predictions.

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Mathematics Subject Classification: 65M12, 65M60, 76D05, 76F65.

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